Basic properties
| Modulus: | \(1169\) | |
| Conductor: | \(1169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(498\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1169.n
\(\chi_{1169}(3,\cdot)\) \(\chi_{1169}(12,\cdot)\) \(\chi_{1169}(19,\cdot)\) \(\chi_{1169}(24,\cdot)\) \(\chi_{1169}(31,\cdot)\) \(\chi_{1169}(33,\cdot)\) \(\chi_{1169}(38,\cdot)\) \(\chi_{1169}(47,\cdot)\) \(\chi_{1169}(54,\cdot)\) \(\chi_{1169}(61,\cdot)\) \(\chi_{1169}(66,\cdot)\) \(\chi_{1169}(75,\cdot)\) \(\chi_{1169}(87,\cdot)\) \(\chi_{1169}(89,\cdot)\) \(\chi_{1169}(94,\cdot)\) \(\chi_{1169}(96,\cdot)\) \(\chi_{1169}(108,\cdot)\) \(\chi_{1169}(115,\cdot)\) \(\chi_{1169}(122,\cdot)\) \(\chi_{1169}(124,\cdot)\) \(\chi_{1169}(150,\cdot)\) \(\chi_{1169}(152,\cdot)\) \(\chi_{1169}(157,\cdot)\) \(\chi_{1169}(171,\cdot)\) \(\chi_{1169}(173,\cdot)\) \(\chi_{1169}(178,\cdot)\) \(\chi_{1169}(185,\cdot)\) \(\chi_{1169}(192,\cdot)\) \(\chi_{1169}(194,\cdot)\) \(\chi_{1169}(199,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{249})$ |
| Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((836,673)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{29}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1169 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{160}{249}\right)\) | \(e\left(\frac{337}{498}\right)\) | \(e\left(\frac{71}{249}\right)\) | \(e\left(\frac{257}{498}\right)\) | \(e\left(\frac{53}{166}\right)\) | \(e\left(\frac{77}{83}\right)\) | \(e\left(\frac{88}{249}\right)\) | \(e\left(\frac{79}{498}\right)\) | \(e\left(\frac{29}{249}\right)\) | \(e\left(\frac{479}{498}\right)\) |